AN EFFICIENT STEP METHOD FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DELAY

Diana Otrocol; Marcel-Adrian Şerban

doi:10.11948/2018.498

2018 Volume 8 Issue 2

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Diana Otrocol, Marcel-Adrian Şerban. AN EFFICIENT STEP METHOD FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 498-508. doi: 10.11948/2018.498

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Diana Otrocol, Marcel-Adrian Şerban. AN EFFICIENT STEP METHOD FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 498-508. doi: 10.11948/2018.498

AN EFFICIENT STEP METHOD FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DELAY

1 "T. Popoviciu" Institute of Numerical Analysis, Romanian Academy, Fântanele 57, 400110 Cluj-Napoca, Romania;
2 Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu 25, 400027 Cluj-Napoca, Romania;
3 Department of Mathematics, "Babeş-Bolyai" University, M. Kogălniceanu 1, RO-400084 Cluj-Napoca, Romania

Abstract

Abstract

Using the step method, we study a system of delay differential equations and we prove the existence and uniqueness of the solution and the convergence of the successive approximation sequence using the Perov's contraction principle and the step method. Also, we propose a new algorithm of successive approximation sequence generated by the step method and, as an example, we consider some second order delay differential equations with initial conditions.
- System of delay differential equations /
- step method /
- Picard operators /
- generalized fibre contraction principle
MSC: 47H10;47N20;45G10;45G15

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References

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